the manufacturing supports and the workpiece. These factors are unfavorable for the milling, due to
the bending of the flexible part, and thus vibrations can appear between the tool and the part .
This situation generates dimensional deviations and low surface quality . It is then necessary to
understand the vibratory phenomenon in order to anticipate, control and limit it by optimizing cutting
speed and material removal rate [19-21]. Although the printed part is not adaptable because of the
function that it was designed for, the supports can be optimized. They can be used to modify the
mechanical properties of the part that supports the overall system, as sacrificial structures to increase
the stiffness  or a mass damper to adjust the eigenfrequency of the structure . However, in the
digital chain dedicated to additive manufacturing, supports are principally designed to build an
unsupported overhang structure or to limit part distortion. Considering the literature review of Plocher
and Panesar , there is no previous work including the support structure optimization taking into
account all the mechanical loads applied during the post-processing. Indeed, the control of their
equivalent stiffness and their equivalent mechanical properties is not considered. In the same way as
Hussein et al.  proposes to use lattice structures as supports to minimize the lasering time. A novel
approach is to consider lattices structures as supports with the ability to control the mechanical
properties of the overall additive manufacturing part, with the objective of post-processing the
surfaces by milling.
Thus, the present work is proposed to use lattices structures as custom-made supports directly
manufactured during the process. This study highlights the influence of support stiffness on the milling
operation and its effect on the quality of the finished surfaces. Side milling tests are carried out on
plate samples and their manufacturing supports. Support structures with different stiffnesses are
compared, using different geometrical and sizes of support structures. Cutting forces and
displacements are measured using a dynamometric plate and a laser vibrometer. A correlation to the
surface quality is presented.
2. Material and methods
2.1. Geometry and SLM additive manufacturing of the samples
Differences of stability in milling and potential vibration problems are highlighted by the design of
adequate SLM samples. In the previous studies about chatters when machining, milling instability
directly resulted from the thin thickness of thin-walled plates. Thevenot et al.  milled a 1-millimeter
thin wall of steel plate (S235) and Seguy et al.  worked with a 2017 aluminum alloy workpiece with
3 mm in thickness and 20 mm in height.
In the present work, the system is composed of two parts of Ti-6A-l4V. The main deflection of the
plates is due to the open geometry of the supports and their low stiffness. Samples with two subparts
are considered and the geometry of the samples is presented in Figure 2. These two parts are
manufactured on a third block (unrepresented) that allows the clamping of the samples in the
machining center and ensures an embedment of the samples at the base of the support-plate system.
The upper rectangular-shaped plate, 3 mm thickness (l
), 9 mm high (l
) and 9 mm wide (l
), is the
subpart to be finished by machining. The lower part of the samples corresponds to the manufacturing
support. Its thickness is equal to (l
) and the height (l
) to 4.5 mm. As the geometrical shape is fixed,
the sample stiffness is controlled by the geometry and the architecture of the supports. Two families
of structures are considered in this study to cover a large range of stiffness: structures directly exported
from the SLM digital chain and lattices structures, as shown in Figure 2.